Consider the single object allocation problem discussed in the class. A single object needs to be allocated to one of n agents. Each agent has a value , that is, the utility he derives from the object, if given for free. The game is as follows: ? Each player/agent simultaneously announces a non-negative number - call it his bid. Denote the bid by player i as bi ≥ 0. Highest bidder wins the object - in case of a tie, the bidder with the lowest index wins (for instance, if agents 2, 3, 5 have the highest bid, then 2 wins the object). The winner gets the object for free, i.e., does not pay anything. All other agents ( i.e., those who don’t get the object) receive a payment equal to the highest bid amount. A) Formulate the game in Normal Form. B) Verify whether the game has a weak dominant strategy equilibrium. Explain why, or why not .
Consider the single object allocation problem discussed in the class. A single object needs to be allocated to one of n agents. Each agent has a value , that is, the utility he derives from the object, if given for free. The game is as follows:
?
Each player/agent simultaneously announces a non-negative number - call it his bid. Denote the bid by player i as bi ≥ 0.
Highest bidder wins the object - in case of a tie, the bidder with the lowest index wins (for instance, if agents 2, 3, 5 have the highest bid, then 2 wins the object).
The winner gets the object for free, i.e., does not pay anything. All other agents ( i.e., those who don’t get the object) receive a payment equal to the highest bid amount.
A) Formulate the game in Normal Form.
B) Verify whether the game has a weak dominant strategy equilibrium. Explain why, or why not .
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